Le Cam's method is applicable when \(V\)  is a binary set and contains, say, \(P_0\)  and \(P_1\) . In its simplest form, it relies on the inequality (see [1]} or [2]}) \(\mathsf {P}_{\mathsf {e}}(V|X^n) \ge \frac{1}{2} \left[1-{\mathsf {TV}}(P^{\otimes n}_0, P^{\otimes n}_1)\right]\) . Thus, it yields the following lower bound for non-private minimax risk
\(\mathcal {R}_n({\mathcal {P}}, \ell )&\ge \frac{\tau }{2} \left[1-{\mathsf {TV}}(P^{\otimes n}_0, P^{\otimes n}_1)\right]\\& \ge \frac{\tau }{2}\left[1-\frac{1}{\sqrt{2}}\sqrt{nD_{\mathsf {KL}}(P_0\Vert  P_1)}\right], \) 
